How to connect two cylinders with a third one connecting the two?
If I understand you correctly, you are looking for a curve with a bevel object.

When you are in objectmode, i would recommend to start with a bezier curve. go to the curve properties and there you can give it "thinckness" with a so called bevel object(has to be also a curve object). 



I assume that you need a circle for the cilindrical shape of the ray.

you can also change the diameter by adjusting the size of the bevel object. 



for getting sharp angles in your curve you also have to change the handle type of the curves vertices to  vector (Shortcut: V). 
therefore you have to be in editmode:



If you want to connect multiple objects together, select every object you want to join and then press CTRL+J. 

BUT 

It is not possible to "weld" multiple curves together, because a curve vertex can only connect to two curve segments. 



The only way is, to convert the curves to meshes (ALT + C)
and then you are able to connect the parts via mesh modeling.